(Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11....
Transcript of (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11....
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12. LTL and CTL
![Page 4: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/4.jpg)
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![Page 18: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/18.jpg)
Example Petri Net
P = {H, O2, H2O, P3, P4}T = {t, T1, T2}A = {(H2,t), (O2,t), (O2, T1), (t, H2O), (t, P3), (H2O, T2), (T2, P4)}w((H2,t)) = 2, w((t, P3)) = 3, w((O2,t)) = w((O2, T1)) = w((t, H2O)) = w((H2O, T2)) = w((T2, P4)) = 1I(t) = {H, O2}, I(T1) = {O2}, I(T2) = {H2O}O(t) = {P3, H2O}, O(T1) = {}, O(T2) = {P4}
![Page 19: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/19.jpg)
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Example Marked Petri Net
P = {H, O2, H2O, P3, P4}T = {t, T1, T2}A = {(H2,t), (O2,t), (O2, T1), (t, H2O), (t, P3), (H2O, T2), (T2, P4)}w((H2,t)) = 2, w((t, P3)) = 3, w((O2,t)) = w((O2, T1)) = w((t, H2O)) = w((H2O, T2)) = w((T2, P4)) = 1I(t) = {H, O2}, I(T1) = {O2}, I(T2) = {H2O}O(t) = {P3, H2O}, O(T1) = {}, O(T2) = {P4}x = [9, 1, 1, 0, 0] corresponding to places [H, O2, H2O, P3, P4]
![Page 22: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/22.jpg)
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Example Marked Petri NetEnabled transitions in red
![Page 24: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/24.jpg)
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Marking corresponds to [H, O2, H2O, P3, P4]
S0 = [9, 1, 1, 0, 0]S1 = [9, 1, 0, 0, 1]S2 = [9, 0, 1, 0, 0]S3 = [7, 0, 2, 3, 0]S4 = [9, 0, 0, 0, 1]S5 = [7, 0, 1, 3, 1]S6 = [7, 0, 0, 3, 2]
Example Marked Petri Net
![Page 28: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/28.jpg)
Pattern: sequence
![Page 29: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/29.jpg)
Pattern: sequence
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Pattern: sequence
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Pattern: sequence
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Pattern: sequence
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Pattern: sequence
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Pattern: sequence
S0 = [2, 0, 0]S1 = [1, 1, 0]S2 = [1, 0, 1]S3 = [0, 2, 0]S4 = [0, 1, 1]S5 = [0, 0, 2]
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Pattern: split
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Pattern: split
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Pattern: split
![Page 38: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/38.jpg)
Pattern: split
S0 = [1, 0, 0]S1 = [0, 1, 1]
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Pattern: join
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Pattern: join
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Pattern: join
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Pattern: join
S0 = [1, 1, 0]S1 = [0, 0, 1]
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Pattern: conflict, choice, decision
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Pattern: conflict, choice, decision
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Pattern: conflict, choice, decision
![Page 46: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/46.jpg)
S0 = [1, 0, 0]S1 = [0, 0, 1]S2 = [0, 1, 0]
Pattern: conflict, choice, decision
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parallel indepencence, confluence
![Page 48: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/48.jpg)
parallel indepencence, confluence
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parallel indepencence, confluence
![Page 50: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/50.jpg)
parallel indepencence, confluence
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parallel indepencence, confluence “diamond” pattern
S0 = [1, 0, 1, 0]S1 = [0, 1, 1, 0]S2 = [1, 0, 0, 1]S3 = [0, 1, 0, 1]
![Page 52: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/52.jpg)
critical section, semaphore, mutex
![Page 53: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/53.jpg)
critical section, semaphore, mutex
![Page 54: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/54.jpg)
critical section, semaphore, mutex
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critical section, semaphore, mutex
![Page 56: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/56.jpg)
critical section, semaphore, mutex
S0 = [1, 0, 1, 0, 1]S1 = [1, 0, 0, 1, 0]S2 = [0, 1, 0, 0, 1]
![Page 57: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/57.jpg)
critical section, semaphore, mutex
S0 = [1, 0, 1, 0, 1]S1 = [1, 0, 0, 1, 0]S2 = [0, 1, 0, 0, 1]
[*, 1, *, 1, *]reachable in some path?
![Page 58: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/58.jpg)
Infinite Capacity Petri net
![Page 59: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/59.jpg)
Infinite Capacity Petri net
S0 = [0, 0]S1 = [ω, 0]S2 = [ω, ω]
![Page 60: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/60.jpg)
Finite Capacity Petri net (FCPN)
![Page 61: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/61.jpg)
Finite Capacity Petri net (FCPN)
S0 = [0, 0]S1 = [1, 0]S2 = [2, 0]S3 = [0, 1]S4 = [1, 1]S5 = [2, 1]
![Page 62: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/62.jpg)
Finite Capacity Petri net as Infinite Capacity net
![Page 63: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/63.jpg)
![Page 64: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/64.jpg)
P/T PN with Inhibitor Arc (makes Turing equiv.)
![Page 65: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/65.jpg)
P/T PN with Inhibitor Arc (makes Turing equiv.)
S0 = [2, 0, 0]S1 = [1, 0, 1]S2 = [0, 0, 2]
![Page 66: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/66.jpg)
P/T PN with Inhibitor Arc (finite capacity)
![Page 67: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/67.jpg)
(ω)
![Page 68: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/68.jpg)
modelling the “current state” → single token
Finite State Automaton represented as a Petri Net
S0 = [1, 0, 0, 0, 0, 0]S1 = [0, 0, 0, 0, 0, 1]S2 = [0, 0, 1, 0, 0, 0]S3 = [0, 1, 0, 0, 0, 0]S4 = [0, 0, 0, 1, 0, 0]S5 = [0, 0, 0, 0, 1, 0]
[0c, 10c, 20c, 30c, 40c, 50c]
![Page 69: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/69.jpg)
![Page 70: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/70.jpg)
FSA without output
![Page 71: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/71.jpg)
FSA with output
![Page 72: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/72.jpg)
![Page 73: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/73.jpg)
Simple Server/Queue
![Page 74: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/74.jpg)
Simple Server/Queue
S0 = [0, 1, 0]S1 = [ω, 1, 0]S2 = [ω, 0, 1]
[queue, idle, busy]
![Page 75: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/75.jpg)
Simple Server/Queuedeparture modelled explicitly
![Page 76: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/76.jpg)
Simple Server/Queuewith server breakdown (and repair)
![Page 77: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/77.jpg)
Simple Server/Queuewith server breakdown (and repair)
![Page 78: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/78.jpg)
![Page 79: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/79.jpg)
![Page 80: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/80.jpg)
Single transmitter
![Page 81: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/81.jpg)
Single transmitter
![Page 82: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/82.jpg)
Single transmitter
![Page 83: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/83.jpg)
Single transmitter
![Page 84: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/84.jpg)
Single transmitter
![Page 85: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/85.jpg)
Two independent transmitters
![Page 86: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/86.jpg)
Two transmitters competing for a single communication channel
![Page 87: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/87.jpg)
![Page 88: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/88.jpg)
![Page 89: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/89.jpg)
Bounded vs. Unbounded
![Page 90: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/90.jpg)
Conservation (invariants)
Sum of busy and idle marking is constant across all sample paths
![Page 91: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/91.jpg)
Conservation (invariants): weighted sum
2 x transmitting + 1 x idle + 1x commChannel = 2
![Page 92: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/92.jpg)
![Page 93: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/93.jpg)
![Page 94: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/94.jpg)
Deadlock in queueing system with rework
[queueFree, queue, rework] = [0, 1, 1] → deadlock
![Page 95: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/95.jpg)
Deadlock in queueing system with rework
[queueFree, queue, rework] = [0, 1, 1] → deadlock
![Page 96: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/96.jpg)
Deadlock in queueing system with rework
[queueFree, queue, rework] = [0, 1, 1] → deadlock
![Page 97: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/97.jpg)
Deadlock resolved (avoided)
![Page 98: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/98.jpg)
Deadlock resolved (avoided)
![Page 99: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/99.jpg)
![Page 100: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/100.jpg)
Liveness example
![Page 101: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/101.jpg)
Liveness example
T1 is L1-liveT2 is deadT3 is L3-live, not L4-live
![Page 102: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/102.jpg)
Liveness example
T1 is L1-liveT2 is deadT3 is L3-live, not L4-live
S0 = [1, 0]S1 = [0, 1]
![Page 103: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/103.jpg)
![Page 104: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/104.jpg)
![Page 105: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/105.jpg)
![Page 106: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/106.jpg)
![Page 107: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/107.jpg)
Fairness
![Page 108: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/108.jpg)
Time
![Page 109: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/109.jpg)
Colour
![Page 110: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/110.jpg)
![Page 111: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/111.jpg)
![Page 112: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/112.jpg)
![Page 113: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/113.jpg)
Coverability Example
![Page 114: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/114.jpg)
Coverability Example
![Page 115: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/115.jpg)
![Page 116: (Place/Transition) Petri Netsmsdl.cs.mcgill.ca/.../lectures/presentation.PetriNets.pdf · 2020. 11. 4. · (Place/Transition) Petri Nets. 12. LTL and CTL. Example Petri Net P = {H,](https://reader033.fdocuments.us/reader033/viewer/2022053121/60a51df214a0bc05e3305a18/html5/thumbnails/116.jpg)
Path Conditions: LTL and CTL